{"paper":{"title":"Towards the classification of homogeneous third-order Hamiltonian operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.DG","math.MP","nlin.SI"],"primary_cat":"math-ph","authors_text":"E.V. Ferapontov, M.V. Pavlov, R.F. Vitolo","submitted_at":"2015-08-11T21:28:00Z","abstract_excerpt":"Let $V$ be a vector space of dimension $n+1$. We demonstrate that $n$-component third-order Hamiltonian operators of differential-geometric type are parametrised by the algebraic variety of elements of rank $n$ in $S^2(\\Lambda^2V)$ that lie in the kernel of the natural map $S^2(\\Lambda^2V)\\to \\Lambda^4V$. Non-equivalent operators correspond to different orbits of the natural action of $SL(n+1)$. Based on this result, we obtain a classification of such operators for $n\\leq 4$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.02752","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}